Definition. Archive score envelope [ftip-00ER]
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    Let \(\mathcal T=\{t_1,\ldots ,t_N\}\) be a finite task set with \(N=|\mathcal T|\geq 1\). For every chain \(a\) in the finite archive, let \(s_i(a)\in \mathbb R\) be its score on task \(t_i\) under a declared common evaluation law. Define its whole-chain mean by

    \[J(a)=N^{-1}\sum _{i=1}^N s_i(a).\]

    For a nonempty archive \(\mathcal A_D\), its archive envelope is

    \[J_D^{\max }=\max _{a\in \mathcal A_D}J(a).\]

    The finite real-valued maximum is attained by at least one archived chain. It scores a single chain across all tasks; it does not select a different chain for each task.

    Deployment eligibility is a separate condition. A target configuration specifies which recorded chains can execute with their stated behavior and resource requirements. Maximizing over that eligible subset gives a deployable archive choice when the subset is nonempty; if it is empty, there is no eligible archived choice. Applying the recorded score to deployment additionally requires the same evaluation law. Records from different configurations alone do not establish these conditions.